types of similar figures

1) Identifying similar figures

2) Calculating scale factor

3) Finding a missing measurement​

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identifying similar figures

Remember that similar figures must have two qualities:

1) Their angles must be congruent (equal or the same)

2) Their sides must be proportional (shrinking or growing by the same amount)​

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1) Identify the corresponding sides (longest with longest, shortest with shortest)

2)​ Set up a proportion (Butterfly ratios)

3) ​Cross multiply the wings.

4) If the wings are equal, the figures are similar.​

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In this example, the wings are not equal, so these figures are not similar.​

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To determine if two figures are similar:

calculating scale factor

Scale factor is the ratio by which the sides of a figure are increased or decreased. Scale factors are multiplied by.

Scale factor is written as

model : actual or model/actual (model divided by actual)​

It can also be written as

new : original or new/original ​

Let's look at some examples​.

(SIMPLIFY YOUR SCALE FACTORS)

In the first example, the new triangle has a size of 2 units and the original has a size of 1 unit. The scale factor is 2:1.

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In the second example, the new triangle has a size of 1 unit and the original has a size of 2 units. The scale fact is 1/2.

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here are two examples

Another example:

The scale of model:actual for the model cars that jeff is creating is 1:5. What does this mean?

This means that when the model is 1 unit, the actual car is 5 units.​

To do this, create a proportion.

Cross multiply and solve for the variable.​

In this example, we can set up a proportion of inches over miles. Then, we cross multiply and find out there are 1, 320 miles between the two countries.

You can use scale factor to find missing measurements.

Finding the missing measurement:

To find missing measurements:

1) Identify the corresponding sides (longest with longest, shortest with shortest)

2) SET UP A PROPORTION (butterfly method)

3) Cross multiply and solve for missing measurement ​

In the example, the butterfly method was used to find the missing side.

In rectangle A, the long side over the short side = 6/4. In rectangle B, the long side over short side = x/10. The same side should be at the same spot in each proportion.

Example:

If you see a problem that combines more than one triangle into one shape, redraw the triangles as two separate triangles.

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Then, use the butterfly method to find the missing side.​

Combined triangles

If you see a problem that combines more than one triangle into one shape, redraw the triangles as two separate triangles.

Then, use the butterfly method to find the missing side.​

For the bigger triangle, be sure to add the two numbers on the long side.​

Combined triangles